### Abstract

A consistent loop expansion around Parisi's replica symmetry breaking mean field theory for the Ising spin glass is constructed. Above the upper critical dimension d = 6 the short range corrections can be absorbed into the parameters of a Ginzburg-Landau type free energy functional whereby the d < ∞ dimensional theory can be mapped back onto mean field theory. For d > 8 the map is regular, thus mean field exponents are preserved, only prefactors are modified. For 6 < d < 8 the order parameter and the spectrum acquire non-trivial exponents which can still be calculated exactly. In the limit d →6 + 0 scaling is restored.

Original language | English |
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Pages (from-to) | 295-304 |

Number of pages | 10 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 185 |

Issue number | 1-4 |

DOIs | |

Publication status | Published - jún. 15 1992 |

### ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics

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## Cite this

Kondor, I., De Dominics, C., & Temesvári, T. (1992). Short range corrections to the order parameter and to the excitation spectrum of the Ising spin glass.

*Physica A: Statistical Mechanics and its Applications*,*185*(1-4), 295-304. https://doi.org/10.1016/0378-4371(92)90468-6